Solve zx^2+yx=0

$$z { x }^{ 2 } +yx=0$$

Solve for y

$$\left\{\begin{matrix}\\y=-xz\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract zx^{2} from both sides. Anything subtracted from zero gives its negation.

$$yx=-zx^{2}$$

Reorder the terms.

$$xy=-zx^{2}$$

Divide both sides by x.

$$\frac{xy}{x}=-\frac{zx^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$y=-\frac{zx^{2}}{x}$$

Divide -zx^{2} by x.

$$y=-xz$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-\frac{y}{z}\text{, }&z\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }z=0\end{matrix}\right.$$